Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x - 8$ and $ KL = 7x - 12$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x - 8} = {7x - 12}$ Solve for $x$ $ -2x = -4$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({2}) - 8$ $ KL = 7({2}) - 12$ $ JK = 10 - 8$ $ KL = 14 - 12$ $ JK = 2$ $ KL = 2$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {2} + {2}$ $ JL = 4$